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Let A={1,\ 2,\ 3} . Then, the number of ...

Let `A={1,\ 2,\ 3}` . Then, the number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is (a) 1 (b) 2 (c) 3 (d) 4

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

R is reflexive `rArr (1,1),(2,2),(3,3) in A`
R is symmetic `rArr (1,2),(2,1) in R`
`and (1,3),(3,1) in R`
R is not transitive `rArr (3,1),(1,2) in R`
but `(3,2) in R`
`therefore (3,2) in R and (2,3)j in R`
Therefore number of required relations =1
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NAGEEN PRAKASHAN ENGLISH-RELATIONS AND FUNCTIONS -Miscellaneous Exercise
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  17. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

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  18. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

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